To explain the observed multiwavelength emission from the cataclysmic variable star AE Aquarii, we propose a model based upon the assumption that the compact component of this binary consists of a white dwarf with a surface field strength of 1 MG, rotating through a clumpy ring near the circularization radius. We argue that MHD instabilities like the Kelvin–Helmholtz instabilities will result in the white dwarf field mixing with the gas in this region and becoming highly sheared. The Poynting flux pumped into the region, and hence angular momentum transferred in the process, is enough to accelerate material centrifugally from the system. We also show that magnetic reconnection in this region will result in runaway electron acceleration to energies of 300 MeV or more, which will radiate through the synchrotron process up to frequencies of the order of ν∼1015 Hz. We show that, because the radiation is emitted in a gaseous medium, the spectrum will be suppressed below the so-called Razin–Tsytovich frequency, which is νR∼2000 GHz, which agrees with the observations. Magnetic shear in the ejection region will also induce field-aligned currents in the magnetosphere. Huge potential differences (double layers) can be generated in the circuit where the gas density becomes very low. This will occur close to the white dwarf. In this region potentials of the order of Φ∥=300 TV (TV = teravolt) can be generated. Synchrotron losses on electrons will restrict them to energies of the order of ℰ50 keV. As protons and ions are not affected by synchrotron losses, energies in excess of 1 TeV are possible. Very high-energy (VHE) γ-ray emission can be produced if these proton and ion beams collide with the clumpy gas in, or outside, the ejection zone. We show that pulsed VHE γ-ray emission is possible, if the gas particle density of the target matter Ng>1013 cm−3, which is compatible with the typical gas particle densities Ng∼1016 cm−3 of the blobs inside the clumpy accretion stream from the secondary star. We show that the VHE γ-ray bursts that were reported by two groups can be explained in terms of an exploding double layer, which will result in a cataclysmic burst of VHE protons and ions over short time-scales. The total power released in the process can be Pγ,b∼1034 erg s−1, which is equal to the spin-down power of the white dwarf, and is enough to explain the reported VHE γ-ray bursts. This implies that the whole reservoir of spin-down power has gone into the production of VHE particles and γ-ray emission.